I have downloaded old versions of Xcode and macOS so I could develop and test an app on my old 1st-gen iPad device.
I wonder if I can submit a new app which runs on iPad 1 (iOS 5) to Apple App Store as of 2017?
32-bit apps will be rejected, but that's not the whole story. Providing the app supports 64-bit, you can provide a 32-bit version alongside in the same app bundle. This way there is a 64-bit version for newer devices/iOS (iOS 11 removes 32-bit app support), but also a 32-bit version for older devices.
To add 32-bit and 64-bit support to your app bundle in Xcode, you need:
You can then build your app to support 32-bit and 64-bit which will successfully submit to iTunes Connect.